The following description of the background of the invention is provided simply as an aid in understanding the invention and is not admitted to describe or constitute prior art to the invention.
Polymerase chain reaction (PCR), is an in vitro enzymatic reaction for the amplification of a target nucleic acid (NA). PCR is commonly carried out as a thermally cyclical reaction; that is, a reaction tube is heated and cooled to achieve the temperatures required at each step of a replication reaction in a single PCR cycle. After each replication cycle, the generated NA itself becomes a template for replication in subsequent cycles. Thus, target NA in a sample grows exponentially over the course of repeated cycles. With PCR it is possible to amplify from as little as one or a few copies of a target NA to amounts several orders of magnitude greater.
Quantitative PCR (QPCR), also known as real-time PCR, typically utilizes fluoresce-based detection methods to monitor the quantity of a target NA after each amplification cycle. Various methods have been reported for analyzing signal indicative of the amount of amplicon at each cycle generated from such experiments. Perhaps most common are variations of the threshold (Ct) standard curve method. In this method, the generated signal is analyzed to determine a fractional cycle number that is related to initial template concentration. One example of such a method is described in U.S. Pat. No. 6,303,305 (Wittner et. al.).
Mathematical descriptions of the chemical reactions of a PCR cycle have also been reported. For example, Stolovitzky and Cecchi, Proc. Natl. Acad, Sci. 1996, 93:12947-52 described one mathematical model of the amplification efficiency of DNA replication in PCR developed from considering the kinetics of the chemical reactions involved.